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# Zero Order Reaction - Practice Questions & MCQ

Edited By admin | Updated on Sep 18, 2023 18:35 AM | #JEE Main

## Quick Facts

• Zero Order Kinetics - Zero Order Reaction, Integrated Rate Law - Zero Order Reaction, Half Life and Life Time of Reaction, Graphs for Zero-Order Reaction is considered one of the most asked concept.

• 55 Questions around this concept.

## Solve by difficulty

Units of the rate constant of first and zero-order reactions in terms of molarity M unit are respectively.

The unit of rate constant and rate of reaction are the same for

In a reaction, $\mathrm{2X_2 + Y_2 \rightarrow 2X_2Y,}$  the X disappears at

For a zero order reaction, $\mathrm{K}=2 \times 10^{-3} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}$ . If initial concentration of the reactant is 1.0 mol $\mathrm{L^{-1}}$  the concentration after 5 minutes would be

For a zero order reaction, which of the following expressions correctly represents the reaction?

A substance, having initial concentration Ao, reacts according to zero order kinetics. The time it takes for the completion of the reaction is -  (Take rate constant as K)

Identify the correct statement in respect of zero order reaction

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For a zero order reaction, if initial concentration is reduced to ½ of the initial concentration, the time taken for half the reaction to complete

The half life of a chemical reactant is 20 minutes at a certain initial concentration. When concentration is reduced to one-half, half life is observed to be 10 minutes. Order of reaction is

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Numerical value of Rate constant of a chemical reaction is given as

 Time (s) 0 5 10 15 Rate 0.003 0.003 0.003 0.003

Which among the following may be the order of the reaction?

## Concepts Covered - 5

Zero Order Kinetics - Zero Order Reaction

Zero order Reactions

In such reactions rate of reaction is independent of concentration of the reactants.

$\mathrm{Rate \propto [concentration]^0}$
For example, suppose we have a reaction

$\mathrm{A \longrightarrow B}$

then, the rate of reaction can be written as

$\mathrm{Rate = -\frac{dA}{dt}=k [A]^0}$

From the above equation it is evident that for a Zero order reaction,

(1) The rate of reaction is equal to the rate constant

(2) The rate of reaction is constant and independant of time

(3) The unit of rate constant is $\mathrm{mol L^{-1} time^ {-1}}$

(4) The rate of reaction cannot be changed by changing the concentration of reactant.

Integrated Rate Law - Zero Order Reaction

Integrated Rate law for a Zero Order reaction

Zero order reaction means that the rate of the reaction is proportional to zero power of the concentration of reactants. Consider the reaction,

$\mathrm{A\rightarrow P}$

$\text { Rate }=-\frac{\mathrm{d}[\mathrm{A}]}{\mathrm{dt}}=\mathrm{k[A]^{0}}$

$\Rightarrow\text { Rate }=-\frac{\mathrm{d}[\mathrm{A}]}{\mathrm{dt}}=\mathrm{k}$

$\Rightarrow \mathrm{d[A]\: =\: -kdt}$

$\Rightarrow \mathrm{\int _{[A_0]}^{[A_t]}d[A]\: =\: -k\int _0^tdt}$
Thus, on integrating both sides, we get:

$[\mathrm{A_t}]=[\mathrm{A]_{0}}\mathrm{-kt}$

Comparing the above equation with the equation of a straight line, y = mx + c, if we plot [A] against t, we get a straight line as shown in the above figure with slope = –k and intercept equal to [A]o.

Half Life and Life Time of Reaction

Half-life of reaction:

The half-life of a reaction is the time in which the concentration of a reactant is reduced to half of its initial concentration. It is represented as t1/2.
For a zero order reaction, rate constant is given as follows:

$\mathrm{A_t= A_0 - kt}$
$\mathrm{When\ t= t_{\frac{1}{2}}, [A]_t=\frac{[A]_0}{2}}$
Putting these values in the integrated rate expression,

$\mathrm{\frac{[A]_0}{2}=[A]_0 - kt_\frac{1}{2}}$

Upon solving the above expression we have,
$\mathrm{t_{\frac{1}{2}}=\frac{[A]_0}{2k}}$
Thus, it is clear that half life for a zero order reaction is directly proportional to the initial concentration of the reactants and inversely proportional to the rate constant.

Life time of Reaction: It is time in which 100% of the reaction completes. It is represented as tLF.
Thus, at t = tLF, A = 0
Now, from integrated rate equation for zero order, we know:

$\mathrm{A\: =\: A_{o}\: -\: kt}$

$\mathrm{0\: =\: A_{o}\: -\: kt_{LF}}$

$\mathrm{Thus, t_{LF}\: =\:\frac{A_{o}}{k}}$

Graphs for Zero-Order Reaction

Special Zero Order Reaction

This concept can be understood by the following example:

Example:
The reaction occurs as follows:
$\mathrm{3A\: \rightarrow \: P}$
Initial concentration of A is given as and rate of the reaction(r) is given as k[A]o. Find the concentration of A after time 't' and also determine the half life of A.

Solution:
For zero-order reaction, the rate equation is given as follows:

$\mathrm{A\: =\: A_{o}-kt}$

According to question, we have given:

$\mathrm{r\: =\: k[A]^{0}\: =\: -\frac{1}{3}\frac{dA}{dt}}$

$\mathrm{-\frac{1}{3}\frac{dA}{dt}\: =\: k\quad\quad\quad\quad\quad(Since\: [A]^{0}\: =\: 1)}$

Now, integrating both sides we get:

$\mathrm{[A]^{A}_{A_{o}}\: =\: -3k(t)^{t}_{o}}$

$\mathrm{A-A_{o}\: =\: -3kt}$

$\mathrm{\mathbf{A\: =\: A_{o}-3kt}}$
This is the concentration of A after time 't'.

Now, for zero-order reaction, the half-life of a reaction is given as below:

$\mathrm{t_{1/2}\: =\: \frac{A_{o}}{2k}\: =\: \frac{A_{o}}{2(3k)}}$

$\mathrm{Thus,\: \mathbf{t_{1/2}\:=\: \frac{A_{o}}{6k}}}$
This is the half-life of A for this reaction.

## Study it with Videos

Zero Order Kinetics - Zero Order Reaction
Integrated Rate Law - Zero Order Reaction
Half Life and Life Time of Reaction

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